Answer:
x = 3.499 in
Step-by-step explanation:
In a kite, the diagonals are perpendicular. Hence [tex]\Delta DOC[/tex] is a right angled triangle.
[tex]DC=7\text{ }in,\text{ }OC=5\text{ }in[/tex]
From Pythagoras theorem, since [tex]\Delta DOC[/tex] is a right angled triangle, [tex]DO^{2}+OC^{2}=DC^{2}[/tex].
Area of [tex]\Delta DOC[/tex] = [tex]\frac{1}{2}\times base\times height[/tex]
[tex]=\frac{1}{2}\times DO\times OC=\frac{1}{2}\times OP\times DC\\(2\sqrt{6})\times(5)=(7)\times(OP)\\OP=3.499\text{ }in[/tex]
From diagram [tex]OP=x[/tex]
∴ [tex]x=3.499\text{ }in[/tex]
